## Abstract

In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real matrix and x and b are n-vectors. Assume that an approximate solution x is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for ∥A^{-1} b - x̃∥_{∞}. The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with 2/3n^{3} flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations.

Original language | English |
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Pages (from-to) | 755-773 |

Number of pages | 19 |

Journal | Numerische Mathematik |

Volume | 90 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 Feb 1 |

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics